Four small spheres, each of which you can regard as a point of mass 0.200 kgkg, are arranged in a square 0.400 mm on a side and connected by light rods. Find the moment of inertia of the system about an axis through the center of the square, perpendicular to its plane. Find the moment of inertia of the system about an axis bisecting two opposite sides of the square. Find the moment of inertia of the system about an axis that passes through the centers of the upper left and lower right spheres and through point O.
Rigid Body
A rigid body is an object which does not change its shape or undergo any significant deformation due to an external force or movement. Mathematically speaking, the distance between any two points inside the body doesn't change in any situation.
Rigid Body Dynamics
Rigid bodies are defined as inelastic shapes with negligible deformation, giving them an unchanging center of mass. It is also generally assumed that the mass of a rigid body is uniformly distributed. This property of rigid bodies comes in handy when we deal with concepts like momentum, angular momentum, force and torque. The study of these properties – viz., force, torque, momentum, and angular momentum – of a rigid body, is collectively known as rigid body dynamics (RBD).
Four small spheres, each of which you can regard as a point of mass 0.200 kgkg, are arranged in a square 0.400 mm on a side and connected by light rods.
Find the moment of inertia of the system about an axis through the center of the square, perpendicular to its plane.
Find the moment of inertia of the system about an axis bisecting two opposite sides of the square.
Find the moment of inertia of the system about an axis that passes through the centers of the upper left and lower right spheres and through point O.
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